Non-Oberbeck–Boussinesq effects on a differentially heated vertical cavity with high-Prandtl number fluid

Abstract

This study explores the non-Oberbeck–Boussinesq (NOB) effects on hydrodynamics and heat transport in two-dimensional glycerol-filled differentially heated vertical cavity (DHVC). The simulations span Rayleigh numbers (Ra) from 2×103 to 5×109 and temperature difference (Δθ̃) up to 50 K at a Prandtl number (Pr) of 2547. We showed the emergence of stratified flow structures, delineated the NOB effects on temperature distribution symmetry, and analyzed the scaling behaviors of the Nusselt number (Nu), Reynolds number (Re), and thermal boundary layer (BL) thicknesses (λ¯hθ and λ¯cθ) against Ra. For Ra≥3×105, the stratification number (S) shows reduced sensitivity to changes in Ra, stabilizing around 0.5. Additionally, the center temperature (θcen) appears to be unaffected by Ra and increases linearly with Δθ̃ for Ra>106, satisfying θcen≈2.99×10−3K−1Δθ̃. Our results also revealed that Nu∼Raγ Nu and Re∼RaγRe with 0.2649≤γ Nu≤0.2654 and 0.3633≤γ Re≤0.3643, respectively, where γ Nu and γ Re exhibit a monotonic decrease as NOB effects intensify. For all investigated Ra values, NuNOB/NuOB<1 and ReNOB/ReOB>1 hold consistently, with deviations from OB predictions capped at 6.38% and 2.63% for Ra≥108, respectively. The analysis of thermal BL thickness reveals distinct scaling behaviors, characterized by λ¯h,cθ∼Raγ λ¯ h, c, with scaling exponents ranging from −0.2690 to −0.2669 for both OB and NOB scenarios. Notably, it reveals a divergence from water-based DHVC trends, showing linear decreases in the hot wall's scaling exponent and increases for the cold wall.